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MeerKAT Optics Design Isak Theron [email protected] (Dirk de Villiers & Robert Lehmensiek)

Contents • Overview of modelling techniques • Current stage in the KAT project • MeerKAT specification • Questions • Way forward

© EMSS Antennas, 3GC-II 2011

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Modelling Techniques • Computational Electromagnetics – Reasonably mature, more trusted in industry – Significant increase in computing power

• Commercial codes – Testing, validation & maintenance – Documentation

• Different levels of approximation – Method of moments → MLFMM – Physical optics (with diffraction) – Geometrical optics → Aperture integration © EMSS Antennas, 3GC-II 2011

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Method of Moments • Small complex structures, e.g. feed horn • Current flowing on surfaces – Electric current on metal surfaces – Electric and magnetic on dielectric surfaces

• Current expanded as sum of basis functions –

• Entire domain possible • Typically triangular – Very general © EMSS Antennas, 3GC-II 2011

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Method of Moments • Wire segments in 2D • Simple field calculation –

• • • •

Sampled boundary condition (basis function) Dense matrix equation – “Full wave solution” Memory ∝ N2 ∝ f4; Solution time ∝ N3 ∝ f6 Example: FEKO © EMSS Antennas, 3GC-II 2011

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Multilevel Fast Multipole Method • • • • •

Larger problems, e.g. dishes at L-band Group basis function interaction in blocks Iterative solution of sparse matrix Memory / Solution time ∝ N log N ∝ f2 log f Still a full wave solution, same accuracy

© EMSS Antennas, 3GC-II 2011

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Physical Optics • Even larger problems, dishes at X-band • Current approximated from incident field –

• Field calculated from current integral • Can hybrid this with MoM – Modify MoM currents – One directional coupling – Not for large MoM regions © EMSS Antennas, 3GC-II 2011

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Physical Optics, PTD extension • PO current independent of edge effects • Physical theory of diffraction (PTD) correction

© EMSS Antennas, 3GC-II 2011

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Physical Optics • Step-wise approach • Feed → sub-reflector → main reflector → Far field

• Low frequency limit • Example: GRASP9; FEKO (single reflection) © EMSS Antennas, 3GC-II 2011

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Geometrical Optics • Even higher in frequency • Specular reflection / stationary phase Source

Propagation

Field point

Integrate over area

© EMSS Antennas, 3GC-II 2011

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Geometrical Optics • • • •

Rays of expanding cones Reflected tangential to surface normal Ray “density” modified for curved surfaces For dishes – Refined by doing only up to aperture – Example: cassbeam (Walter Brisken)

• Fails if radius of curvature too small • Add diffraction terms – UTD – Same stationary phase concept with edges © EMSS Antennas, 3GC-II 2011

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Modelling software • FEKO – Full wave analysis with MLFMM – Parallelised for large machines (leo cluster with 176 cores, groups of 12 – 32) – Rather expensive if not inside EMSS

• GRASP9 – Full version & multiple GRASP SE installation – 20 000 Euro

• Pick according to frequency range © EMSS Antennas, 3GC-II 2011

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Contents

Current stage in the KAT project

© EMSS Antennas, 3GC-II 2011

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KAT Phases • XDM (Done) • Single antenna HARTRAO • Original KAT = 21 x XDM • KAT-7 (7 antennas in Karoo) • Meant as engineering model

• Being commissioned • MeerKAT (64 antennas in Karoo)

• PDR (July 2011) • Currently finalising dish specification © EMSS Antennas, 3GC-II 2011

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Contents

MeerKAT specification What is fixed

© EMSS Antennas, 3GC-II 2011

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MeerKAT Specifications • Offset Gregorian • Effective focal length / Feed illumination angle – Fixed at Feq/D = 0.55

• Final optics selection – Finalising layout – Mechanical trade-off pending

• Feed low © EMSS Antennas, 3GC-II 2011

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Offset Gregorian Selection • Small dish array – Really compound “per antenna” negative effects – Cannot “copy” conventional wisdom

• Offset Gregorian v. Cassegrain – Cassegrain have narrow feed angles – Decision driven by size of the feed horns

• Offset Gregorian v. Prime focus – Multiple feeds • There is “storage” real estate outside the optical path © EMSS Antennas, 3GC-II 2011

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Offset Gregorian v. Prime Focus • Prime focus feed blockage – Result in gain ripple (re-radiation from feed) – Effect would be smaller on a large dish Inconveniently similar to the primary beam

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Prime Focus (KAT-7) gain ripple

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Offset Gregorian v. Prime Focus

Prime focus

Offset Gregorian (Vertical-pol)

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Offset Gregorian v. Prime Focus • Far out side-lobes (tipping and Tspill-over)

© EMSS Antennas, 3GC-II 2011

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Offset Gregorian v. Prime Focus • Near side-lobes rotational variation 11.5°

© EMSS Antennas, 3GC-II 2011

1.4 GHz

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Offset Gregorian v. Prime Focus • Allow stronger edge illumination • No strut blockage – Ae about 10% higher for same projected area – Clean patterns • RFI reduction • Tsys improvement at lower elevations • Can get low side-lobes (also traded against Tspill)

• Cross-polarisation need not be worse – Reflector orientation (Mitzugutch) – Flatter equivalent system © EMSS Antennas, 3GC-II 2011

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Offset Gregorian Selection • Also not a perfect solution – Mechanical complexity – More surface and cost – Two surfaces contributing to phase (Ruze) error • Offset reduce main reflector impact by 10 - 15%

– Lost sky coverage • Significant impact on simultaneous observation

– Shadowing increase minimum spacing – Requirements of “Phased” array feeds?

• Offset Gregorian still the best option © EMSS Antennas, 3GC-II 2011

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Offset Gregorian Selection Dual offset reflectors Multiple cryogenicallycooled octave-band receivers

Note angle

© EMSS Antennas, 3GC-II 2011

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Feed Angle Selection • Compact 1-1.75 GHz horn • Optimised for dishes with different focal ratios • “Flatter” systems capture less of the feed energy • In deeper systems the feed get in the way of the optical path • Flat optimum Feq/D = 0.5 – 0.6 © EMSS Antennas, 3GC-II 2011

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Feed Angle Selection

Dm = 13.5 m, Feq/D = 0.5 / 0.55

4 3

2 1

0

-1

0.5

-2

0.55 -3

-4 -5

Main reflector diameter = 13.5m x 15.25m

-6 -7 -4

-2

0

2

4

6

8

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MeerKAT Optics Selection • Blank page – Only feeds fixed (by us), dish optics still open – Daunting parameter space • Six degrees of freedom on dual reflector system

– Mechanical trade-off dependent on design • MeerKAT / TDP boom / main reflector length

– Want the best “as built” performance

• Main reflector sized for sensitivity • Sub-reflector sized for road transport • Cross-polarisation (Mitzugutch) © EMSS Antennas, 3GC-II 2011

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MeerKAT optics selection • Sub-reflector clearance increases feed boom length – prefer no clearance 3

2

1

0

-1

-2

-3

-4

-5

Main reflector diameter = 13.5m x 15.25m

-6

-7

-4

-2

0

2

4

6

8

10

12

14

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MeerKAT optics selection • Last trade-off Main reflector size v. feed boom length 3

2

Subreflector length = 3.8m

1

0

-1

-2

-3

-4

13.5m x 15.25m (TU.1)

13.5m x 15.85m (TU.3) -5

-6

-7

-2

0

2

4

6

8

10

12

14

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Feed high versus feed low • Feed low – Allows easy access to the feeds – Spill-over better controlled

• “Sail” upright – Not “ideal” stowing

© EMSS Antennas, 3GC-II 2011

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Feed high versus feed low

© EMSS Antennas, 3GC-II 2011

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Feed high versus feed low

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Feed high versus feed low Tspillover tipping curve 9

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Feed low, default Feed high, default Feed low, with extension

Noise temperature [K]

7

6

5

4

3

2 0

10

20

30 40 50 Angle from zenith [degrees]

© EMSS Antennas, 3GC-II 2011

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70

80

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Contents

Questions What is still undecided

© EMSS Antennas, 3GC-II 2011

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Issues • Shaping – Trade-off between side-lobes and efficiency

• • • •

Designing the extension Beam offset (“Squint” defined otherwise) Tolerance Slots (between panels) impact

© EMSS Antennas, 3GC-II 2011

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Shaping • Increase the parameter space: shaping – Capture more feed energy • Deeper effective system for same feed • Need not increase side-lobes • Typically a small impact on radio astronomy systems

– Distribute pattern to use surface better • Will increase side-lobes

– Much easier to control aperture field • Sensitive to feed pattern – Deep taper sensitive to error in centre of sub-reflector – Hard illumination has spill-over loss and diffraction © EMSS Antennas, 3GC-II 2011

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Shaping

© EMSS Antennas, 3GC-II 2011

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Shaping • Almost no mechanical reflector difference Feed position further from main dish TU.3/TS.3 comparison

3

Less diffraction

2 1

z (m)

0 F0 F0

-1 -2 -3 -4 -5 -6 -4

Shaped Unshaped -2

0

2

4

6

8

10

12

14

x (m)

© EMSS Antennas, 3GC-II 2011

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Designing the extension • • • • • •

Extension primarily to shield spill-over Tend to increase gain Reduce diffraction ripple Increase reflection back to feed Increase cross-polarisation Need further optimisation

© EMSS Antennas, 3GC-II 2011

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Designing the extension TU3 76

a [%]

74 72 70

extend = 0

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extend = 10

66

extend = 20

1000

1100

1200

1300

1400

1500

1600

1700

1800

1100

1200

1300

1400 Frequency [MHz]

1500

1600

1700

1800

-24

SLL [dB]

-26 -28 -30 -32 -34 1000

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Designing the extension Unshaped 76 74

a [%]

72 70 68

extend = 0

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extend = 10

64

extend = 20

62 550

600

650

700

600

650

700

750

800

850

900

950

1000

850

900

950

1000

-22 -24

SLL [dB]

-26 -28 -30 -32 -34 550

750 800 Frequency [MHz]

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Designing the extension TS3 77

extend = 0

a [%]

76

extend = 20

75 74 73 72 1000

1100

1200

1300

1400

1500

1600

1700

1800

1100

1200

1300

1400 Frequency [MHz]

1500

1600

1700

1800

-24

SLL [dB]

-26 -28 -30 -32 -34 1000

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Designing the extension TS3

extend = 0

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extend = 20

a [%]

74

72

70

68 550

600

650

700

600

650

700

750

800

850

900

950

1000

850

900

950

1000

-22 -24

SLL [dB]

-26 -28 -30 -32 -34 -36 550

750 800 Frequency [MHz]

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Designing the extension TS3e20 85 Vertical Horizontal

 a [%]

80

75

70

65 1000

1100

1200

1300

1400

1500

1600

1700

Frequency [MHz]

© EMSS Antennas, 3GC-II 2011

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Designing the extension TS3e20 85 Vertical Horizontal

 a [%]

80

75

70

65

600

650

700

750

800

850

900

950

1000

Frequency [MHz]

© EMSS Antennas, 3GC-II 2011

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Designing the extension TS3e20 -20 Vertical (-1 dB) Horizontal (-1 dB) Vertical (-3 dB) Horizontal (-3 dB)

-22

-24

Jones cross-pol [dBr]

-26

-28

-30

-32

-34

-36

-38

-40 1000

1100

1200

1300

1400

1500

1600

1700

Frequency [MHz]

© EMSS Antennas, 3GC-II 2011

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Designing the extension TS3e20 -20 Vertical (-1 dB) Horizontal (-1 dB) Vertical (-3 dB) Horizontal (-3 dB)

-22

-24

Jones cross-pol [dBr]

-26

-28

-30

-32

-34

-36

-38

-40

600

650

700

750

800

850

900

950

1000

Frequency [MHz]

© EMSS Antennas, 3GC-II 2011

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Beam offset • Beam offset that decrease with frequency – Due to reflected angle ≠ incident angle

• Oscillating behaviour – Due to diffraction from sub-reflector -5 mm local x

+5 mm local z

SR -5 mm global x

400

400

300

300

300

200 100 0 -100 560

200 100 0 -100

580

600 620 640 Frequency (MHz)

660

680

200 100 0 -100

1360 1380 1400 1420 1440 1460 1480 Frequency (MHz)

-5 mm local x: offset by 151 arcsec 20

Squint angle (arcsec)

400

Squint angle (arcsec)

(a)

Squint angle (arcsec)

No shift

+5 mm local z: offset by 1 arcsec

© EMSS Antennas, 3GC-II 2011 10

2340 2360 2380 2400 2420 2440 Frequency (MHz) SR -5 mm global x: offset by -217 arcsec 10

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Tolerance • Surface RMS accuracy – Reduce efficiency (Ruze) – Cause variation between beams – Very frequency dependent (1mm at 14.5GHz)

© EMSS Antennas, 3GC-II 2011

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Tolerance • Requirement for beam similarity 18 Maximum error (uniform phase error) Maximum error (weighted phase error) Mean error (uniform phase error) Mean error (weighted phase error)

Beam error relative to ideal beam (%)

16 14 12 10 8 6 4 2 0

0

100

200

300

400 500 600 RMS error (m)

700

© EMSS Antennas, 3GC-II 2011

800

900

1000

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Tolerance • Reduction in efficiency • Edges less illuminated than centre – Weight the outside less than the centre – Kept “loss” per ring constant – Similar to weighting the error with the square root of the aperture voltage pattern

Efficiency if the error applied is to the nth ring only

0.995 0.99

0.985

Efficiency factor

0.98

0.975 0.97

0.965 0.96

Uniform error CEL scaled error AVP scaled error RVP scaled error

0.955 0.95

0.945

0

2

© EMSS Antennas, 3GC-II 2011

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6 Ring number

8

10

12

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Tolerance • Phase error due to length • Oblique incidence

© EMSS Antennas, 3GC-II 2011

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Tolerance 1.6

1.4

Weighting function

1.2

1

0.8

0.6

 towards dish vertex  towards dish high point (away from sub-reflector)  normal to symmetry plane

0.4

Prime focus 0.2

0

1

2

3 4 Aperture radius,  (m)

© EMSS Antennas, 3GC-II 2011

5

6

7

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Tolerance • Effect of alignment – Sensitivity at high frequency – Pointing

• Effect of loading tolerance – Pointing • Can compensate for gravity, not for wind

– Sensitivity – Beam shape and polarimetric variation

© EMSS Antennas, 3GC-II 2011

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Tolerance (TUE.3 and TSE.3)

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Tolerance (TUE.3 and TSE.3)

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Tolerance (TUE.3 and TSE.3)

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Tolerance (TUE.3 and TSE.3)

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Side-lobe specification • -30dB side-lobe requirement at 3° from bore sight (to avoid RFI) difficult for UHF – More or less the first side-lobe – Need interaction here on the advantages / disadvantages

© EMSS Antennas, 3GC-II 2011

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Slots • Slots between dish panels • Quarter-wave “connecting” slots – Narrow band solutions

• Can model with wire grid – 13.5 m prime focus dish with F/D = 0.55 – 2mm wide slots every 1m (not through centre) – MLFMM solution at 580MHz – 25 dB side-lobe at 30°

• Duality - need to work with magnetic fields © EMSS Antennas, 3GC-II 2011

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Slots Gain of a 13.5m prime focus dish with 2mm slots every 1m at 580MHz 40 Dish with slots Dish Wire grid

30

Gain (dB)

20 10 0 -10 -20 -30 -40

0

10

20

30

40

50

60

70

80

90

40 Dish with slots Dish - Wire grid

30

Gain (dB)

20 10 0 -10 -20 -30 -40

0

10

20

30

40 50 Angle  ()

60

70

80

90

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Interpolation • Beam offset vary rapidly with frequency – Causes variation in direction dependent gain

• Base beams from numerical patterns – Slow to compute per frequency – Large amount of data – Need to interpolate – Cannot do so on the beam itself

© EMSS Antennas, 3GC-II 2011

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Interpolation • Interpolation should reflect the physical – Propagation terms – Interpolate between frequencies where k’f is effectively 0° and 90°, i.e. the exponential vary between 1 + j 0 and 0 + j 1 • Linear interpolation of the real and imaginary components yields 0.5 + j 0.5 • Linear interpolation of amplitude and phase yields 0.707 + j 0.707 which, is correct in this case

– Interpolation where the second frequency is effectively n2𝜋 + ∆ is a problem © EMSS Antennas, 3GC-II 2011

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Interpolation • Interpolating 𝜃, ∅ components for linear polarisation on too coarse a grid

© EMSS Antennas, 3GC-II 2011

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Interpolation • Solved three components of the field – Main reflector – Feed – Sub-reflector • Top and bottom are stationary phase points

© EMSS Antennas, 3GC-II 2011

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Contents

Way forward

© EMSS Antennas, 3GC-II 2011

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The near (MeerKAT) future • Finalise the frequency interpolation • Determine basis functions for calibration – Does this influence the design?

• Trade-off of the antenna beam parameters – Aperture efficiency – Spill-over temperature (extension design) – Side-lobe levels (near and far) – Cross-polarisation – Beam roundness © EMSS Antennas, 3GC-II 2011

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Thank you